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//Ex4_18
//Image Smoothing Using Gaussian Lowpass Filter.
// Version : Scilab 5.4.1
// Operating System : Window-xp, Window-7
//Toolbox: Image Processing Design 8.3.1-1
//Toolbox: SIVP 0.5.3.1-2
//Reference book name : Digital Image Processing
//book author: Rafael C. Gonzalez and Richard E. Woods
clc;
close;
clear;
xdel(winsid())//to close all currently open figure(s).
function[H]=lowpassfilter(type1,M,N,D0,n)//lowpassfilter is used to filter an image .
u=0:(M-1);
v=0:(N-1);
idx=find(u>M/2);
u(idx)=u(idx)-M;
idy=find(v>N/2);
v(idy)=v(idy)-N;
[U,V]=meshgrid(v,u);
D=sqrt(U.^2+V.^2);
select type1
case'gaussian'
H=exp(-(D.^2)./(2*(D0^2)));
else
disp('Unknownfiltertype.')
end
endfunction
/////////////////////////////////// Main Programm ////////////////////////////////
a=imread("Ex4_18.tif");
//gray=rgb2gray(a);
gray=im2double(a);
figure,ShowImage(gray,'Gray Image');
title('Original Image');
[M,N]=size(gray);
h=fft2(gray);//fft2() is used to find 2-Dimensional Fast Fourier Transform of an matrix
i=log(1+abs(h));
in=fftshift(i);//fftshift() is used to rearrange the fft output, moving the zero frequency to the center of the spectrum.
inm=mat2gray(in)
figure,ShowImage(inm,'Frequency Spectrum');
title('Frequency Spectrum','color','blue','fontsize',4);
/////////////////////////// Filtering With Cut-off Frequency 10 ///////////////////////
filt=lowpassfilter('gaussian',M,N,10); // Function which generate Filter Mask Corresponding to Low Frequency
//filt_shift=fftshift(filt);
//figure,ShowImage(filt_shift,'Filter Mask');
//title('Filter Mask to Specific Cut-Off Frequency');
n=filt.*h;//Multiply the Original Spectrum with the Filter Mask.
Image_filter=real(ifft(n));
Image_filter=mat2gray(Image_filter)
figure,ShowImage(Image_filter,'Filtered Image');
title('Filtered Image with Cut-Off Frequency 10','color','blue','fontsize',4);
/////////////////////////// Filtering With Cut-off Frequency 30 ///////////////////////
filt=lowpassfilter('gaussian',M,N,30); // Function which generate Filter Mask Corresponding to Low Frequency
//filt_shift=fftshift(filt);
//figure,ShowImage(filt_shift,'Filter Mask');
//title('Filter Mask to Specific Cut-Off Frequency');
n=filt.*h;//Multiply the Original Spectrum with the Filter Mask.
Image_filter=real(ifft(n));
Image_filter=mat2gray(Image_filter)
figure,ShowImage(Image_filter,'Filtered Image');
title('Filtered Image with Cut-Off Frequency 30','color','blue','fontsize',4);
/////////////////////////// Filtering With Cut-off Frequency 60 ///////////////////////
filt=lowpassfilter('gaussian',M,N,60); // Function which generate Filter Mask Corresponding to Low Frequency
//filt_shift=fftshift(filt);
//figure,ShowImage(filt_shift,'Filter Mask');
//title('Filter Mask to Specific Cut-Off Frequency');
n=filt.*h;//Multiply the Original Spectrum with the Filter Mask.
Image_filter=real(ifft(n));
Image_filter=mat2gray(Image_filter)
figure,ShowImage(Image_filter,'Filtered Image');
title('Filtered Image with Cut-Off Frequency 60','color','blue','fontsize',4);
/////////////////////////// Filtering With Cut-off Frequency 160 ///////////////////////
filt=lowpassfilter('gaussian',M,N,160); // Function which generate Filter Mask Corresponding to Low Frequency
//filt_shift=fftshift(filt);
//figure,ShowImage(filt_shift,'Filter Mask');
//title('Filter Mask to Specific Cut-Off Frequency');
n=filt.*h;//Multiply the Original Spectrum with the Filter Mask.
Image_filter=real(ifft(n));
Image_filter=mat2gray(Image_filter)
figure,ShowImage(Image_filter,'Filtered Image');
title('Filtered Image with Cut-Off Frequency 160','color','blue','fontsize',4);
/////////////////////////// Filtering With Cut-off Frequency 460 ///////////////////////
filt=lowpassfilter('gaussian',M,N,460); // Function which generate Filter Mask Corresponding to Low Frequency
//filt_shift=fftshift(filt);
//figure,ShowImage(filt_shift,'Filter Mask');
//title('Filter Mask to Specific Cut-Off Frequency');
n=filt.*h;//Multiply the Original Spectrum with the Filter Mask.
Image_filter=real(ifft(n));
Image_filter=mat2gray(Image_filter)
figure,ShowImage(Image_filter,'Filtered Image');
title('Filtered Image with Cut-Off Frequency 460','color','blue','fontsize',4);
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